If you've never seen the movies, I'd recommend watching them in their release order, but with the film chronology, it seems this is really the truer order of events for the storyline, to me, if you want to follow how apes gained control of the world:
Rise of the Planet of the Apes (2011)
- Action takes place in the 2010s
- Cesar's origin as the infant son of "Bright Eyes" and introduction to the redwood forest at Muir Woods National Monument (this origin is in contradiction to the Cesar origin of Escape from the Planet of the Apes, but that is because this is the original Cesar that learned speech from humans and taught others - not one born to future parents that can already talk)
- Humanity encounters the Simian Flu
Dawn of the Planet of the Apes (2014)
- Action takes place in the 2020s
- Humanity is decimated by the Simian Flu
- Battle between humans in San Francisco and the Apes
Reboot Planet of the Apes (2001)
- Action takes place at first in 2029, close to present-day, then 5021
- Station was presumably launched at the same time the Simian virus was decimating humanity on Earth and as a last-ditch response so that medical research could take place, though this effort is not shown because the movies containing the flu in the storyline had not yet been made.
- Events on the station are either prior to or while the Battle of San Francisco is raging, since the station would have needed to have been launched prior to apes becoming a threat, and the station had not suspended ape escape pod training or taken any extreme measures that one might think would happen when learning that Earth apes had risen up to battle humans.
- Astronaut Leo Davidson and Pericles are catapulted to 5021 when apes rule on a planet where Davidson crashes and eventually Pericles lands. Apes are war-like and have enslaved humans. The planet is largely barren. Wikipedia says the planet is "Ashlar", implying the electromagnetic storm was also a wormhole, but it would make more sense if this was simply an alternate, future Earth that was saved from destruction in 3978 due to the arrival of the Space Station apes in 2029.
- The barrenness of the planet might be explained by a nuclear holocaust, but the apes would likely have to have arrived after the bombs fell to survive. A nuclear war ~2025 would explain this, and also a lack of communication from Earth to the station about the storm and danger of apes.
- Since the introduction of the storm means a new timeline, events in 3978 do not necessarily have to unfold as originally told in Beneath the Planet of the Apes due to the injection of these apes that had been held in captivity, but were now free to kill/enslave humans as they pleased.
Apes that are able to speak in this film are shown to be the descendants of those onboard the crashed Air Force Space Station Oberon "thousands of years ago" to Davidson's time reference, according to his remark when assessing the age of the station and logs, when found. We don't know for sure exactly when the apes landed, but it would have to either be 1) after humans nuked the planet, or 2) before humans made their mark on the world, due to the barrenness of the planet-meaning well before the Middle Ages. I believe it was the former, leading to sometime between 2029-~3000, since the craft was not so old that power had yet fully depleted.
The apes Davidson finds were likely not bred from those that Cesar led in the other films, but a different band altogether, in a different area and era. It might even be a different planet, as Wikipedia suggests, but if this is simply a later Earth, it makes more sense and shows how the storm and station crashing alters the timeline through allowing apes to rise up against and enslave their captors and the natives they encountered when the station crashes down to Earth-perhaps inspiring apes finding Taylor in 3978 to kill him on-sight or be more ruthless, thereby preventing human survivors from hording a doomsday weapon and Taylor from setting it off and destroying the planet.
One more reason I believe this is just an earlier Earth is because the ending has Davidson arriving in a Ape-occupied D.C. back in what looks like the modern age with a General Thade statue (one of the Apes Davidson had met before) sitting where Abraham Lincoln should've been. This could be woven into the timeline by either saying that Davidson actually traveled further into the future where the apes had descendants that eventually rebuilt America, and Davidson and Pericles had set this in motion in the previous time era by saying humans and apes should live together as equals. But otherwise, it would have to either be where General Thade's apes and humans work together to become a space-faring civilization and reach Earth through the same storm as Davidson, but at some time in the mid-1800s, so that the Lincoln Memorial would house General Thade, instead of Lincoln, or Davidson has arrived in an Ape-filled D.C. through a dimensional time-rift that gets him to the right time and back to Earth, but to an incorrect dimension.
Original series timeline
Original series alternate timeline
Escape from the Planet of the Apes (1971)
- Zira and Cornelius arrive in 1973, in the original timeline, from a destroyed Earth, and create an alternate timeline by their actions
- Cesar is born as Zira's infant son
Cesar is traded places with a circus ringleader's monkey, Heloise. Heloise is thrown overboard when Zira and Cornelius are cornered by the military, so the military would believe Cesar was drowned, and the real Cesar could survive.
Conquest of the Planet of the Apes (1972)
- Action takes place in 1993
- Cesar (from Zira and Cornelius) leads his revolt against humans after seeing apes become slaves after dogs and cats die off in 1983 (ten years earlier)
Battle for the Planet of the Apes (1973)
- Post-apocalyptic era - Nuclear war has occurred; action takes place ~2003
- Cesar goes to the Forbidden City (assumed as Los Angeles, from Escape from the Planet of the Apes, since Cornelius and Zira were taken to the L.A. Zoo) to obtain archived records of his parents, and his band is attacked by humans that have survived the nuclear blast
After a final battle with the war-like humans and apes, Aldo, an ape who provoked the apes to attack the humans after the humans declared war, themselves, by killing ape scouts to make it look like the humans did it, is found out by Cesar and dies trying to escape justice. Peace reigns and humans are treated as equals to apes after this event, through at least 2670, when the narrator reveals a statue of Cesar marked AD 2670.
TV Series episodes
The TV series could have easily taken place during the time between the Space Station crash and Davidson's arrival in 5021, putting it between events in the rebooted Planet of the Apes, or set after Battle for the Planet of the Apes, in the given year for the episodes, 3085, giving a person the impression that the peace of 2670 at the end of Battle ultimately failed.
This is just the order I see of how events unfolded, when weaving in the newer movies into the story.